Shaquille Harrison added 14 points, Marquel Curtis 13 and D'Andre Wright 12 for the Golden Hurricane (12-5, 5-0 American Athletic Conference), who won their seventh straight.
Tulsa made half of its 50 shots, was 6 of 10 on 3-pointers and 19 of 22 from the foul line.
South Florida (7-11, 1-4) shot 42 percent, the 12th straight opponent to shoot less than 50 percent against Tulsa. Nehemias Morilla led the Bulls with 15 points.
Tulsa pulled away from a tie at 24 to lead 32-27 at the half.
Woodard hit a 3, Harrison made a layup and Woodard followed with a dunk to make it 57-43 midway through the second half. A 7-0 run that included four Woodard free throws broke it open.